Create a data set with 6 numbers that has a median of 12

Yes, the distribution of a and b is normal, with mean μ=10, median m=10, and standard deviation σ=3.

The resulting distribution of a+b, a-b, a*b, and a/b will also be normal, with the following values:


 
   Operation
   Mean
   Median
   Standard Deviation
 
 
   a+b
   μ=20
   m=20
   σ=√6
 
 
   a-b
   μ=0
   m=0
   σ=√6
 
 
   a*b
   μ=100
   m=100
   σ=30
 
 
   a/b
   μ=3
   m=3
   σ=1
 

Learn more about resulting distribution

brainly.com/question/13634543

#SPJ11

The probability that a person who tests positive actually has the

the disease is, 10%.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

Given, A certain disease has an incidence rate of 0.8%.

Therefore, The probability that a person who tests positive actually has the disease is,

= (8/0.8)%.

= 10%.

learn more about conditional probability here :

https://brainly.com/question/30144287

#SPJ9

The coordinates of B' after the translation represented by (x - 4, y - 3) is (1, -2). See other solutions below

B is located at the point (5, 1) in the figure.

If we translate the point by (x - 4, y - 3), the new location of B, denoted by B', can be found by subtracting 4 from the x-coordinate and 3 from the y-coordinate.

Therefore, B' is located at (1, -2).

The given information provides us with a set of matching points, which are:

Preimage = (2, 1)

Image = (-1, 2)

These points can be represented by the equation:

(x, y) = (-y, x)

This equation indicates that the points have undergone a (d) clockwise rotation of 270 degrees.

Here, the smaller shape is created by scaling down a larger shape, the transformation is a dilation that results in a reduction.

The scale factor for this transformation could be either 1/2 or 1/4.

Given the points P = (3, -2) and S = (4, -5), we apply two transformations.

The first transformation (x - 2, y) is defined as shifting the x-coordinate of each point left by 2 units, while keeping the y-coordinate the same.

This results in new points P' = (1, -2) and S' = (2, -5).

The second transformation involves reflecting the new points across the x-axis, which changes the sign of their y-coordinates.

The resulting points are P'' = (1, 2) and S'' = (2, 5).

In this context, we are given the coordinates of point A as (-2, -5).

This implies that if we scale down the original coordinates by a factor of 1/2, we get the new coordinates of point A, which become (-1, -2.5).

Therefore, the coordinates of point A' are (-1, -2.5).

Read more about transformation at

brainly.com/question/27224272

#SPJ1

In other words, in 100 tyre rotations, the vehicle will have travelled 7,854 inches, or roughly 196.06 feet or 59.79 metres.

The amount of rotations around a central point or axis that a shape or object undergoes is referred to in mathematics as the order of rotation. For illustration, a shape with a 180-degree revolution about its centre has an order of rotation of 2. Similar to this, a shape rotated by 120 degrees has an order of revolution of 3. The idea of rotational symmetry, which describes a property of some shapes and objects that enables them to appear the same after a certain amount of rotation, and the order of rotation are closely related concepts.

given

The circumference of the tyre, which is determined by the following calculation, equals the distance covered by the vehicle in one rotation of its tyres.

C = πd

where the tire's width is d and its circumference is C. Using the tire's circumference of 25 inches as a plug-in, we obtain:

C is 25 times 78.54 inches.

As a result, one tyre rotation on the vehicle will cover a distance of 78.54 inches.

We can easily multiply the distance covered by one tyre rotation by 100 to determine how far the car will drive in 100 rotations:

78.54 inches per revolution times 100 rotations equals 7,854 inches of distance travelled.

In other words, in 100 tyre rotations, the vehicle will have travelled 7,854 inches, or roughly 196.06 feet or 59.79 metres.

To know more about order of rotation visit :-

https://brainly.com/question/28485034

#SPJ1

The Heston stochastic volatility model is a popular model used to describe the dynamics of an asset price in the presence of stochastic volatility. It is a two-factor model that accounts for the random nature of both the asset price and its volatility. The model is given by the following set of stochastic differential equations:

dS(t) = rS(t)dt + Vo(t)S(t)dWi(t)

de(t) = (a – bo(t) dt +0V (t)dWx(t)

where S(t) is the asset price, r is the risk-free rate, V(t) is the stochastic volatility, W1(t) and W2(t) are Brownian motions under the risk-neutral probability measure, and a, b, o are positive constants. The correlation between the two Brownian motions is given by p, which is a constant between -1 and 1.

The Heston model is widely used in finance because it can capture the volatility smile, which is the tendency for options with different strike prices to have different implied volatilities. This feature is important because it allows for more accurate pricing of options and other derivative securities.

To solve the Heston model, we can use the Feynman-Kac theorem, which relates the solution of a stochastic differential equation to the solution of a partial differential equation. This allows us to find the price of an option under the Heston model by solving a partial differential equation. The solution can be found using numerical methods, such as the finite difference method or the Monte Carlo method.

To know more about probability refer here:

https://brainly.com/question/30034780

#SPJ11

The ground distance, given the map distance and the scale, would be 5 kilometers.

If the scale on a map is 1:25,000, it means that one unit of distance on the map represents 25,000 units of distance on the ground. If the map distance is 20 cm, we can find the ground distance as follows:

Convert the map distance from centimeters to kilometers:

20 cm = 0.2 m = 0. 0002 km

Find the ground distance using the scale:

Ground distance = Map distance / Scale

Ground distance = 0. 0002 km / ( 1 / 25,000 )

Ground distance = 0.0002 km x 25,000

Ground distance = 5 km

Find out more on ground distance at https://brainly.com/question/27928319.

#SPJ1

The full question is:

The scale on a map is 1:25,000. Calculate the ground distance if the map distance is 20 cm write your answer in kilometers​

The given set of vectors is: \( \left\{\left[\begin{array}{c}1 \\ 0 \\ -2\end{array}\right],\left[\begin{array}{c}-1 \\ 1 \\ 4\end{array}\right],\left[\begin{array}{c}1 \\ 2 \\ -2\end{array}\right]\right\} \)

To determine if the given set of vectors is linearly independent or linearly dependent, we can use the determinant method. We will form a matrix using the given vectors as columns and then find the determinant of the matrix. If the determinant is zero, then the vectors are linearly dependent. If the determinant is not zero, then the vectors are linearly independent.

The matrix formed using the given vectors as columns is:
\[ \left[\begin{array}{ccc}1 & -1 & 1 \\ 0 & 1 & 2 \\ -2 & 4 & -2\end{array}\right] \]
The determinant of the matrix is:
\[ \begin{vmatrix}1 & -1 & 1 \\ 0 & 1 & 2 \\ -2 & 4 & -2\end{vmatrix} = (1)(1)(-2) + (-1)(2)(-2) + (1)(0)(4) - (1)(2)(4) - (-1)(0)(-2) - (1)(1)(-2) = -2 + 4 + 0 - 8 + 0 + 2 = -4 \]

Since the determinant is not zero, the given set of vectors is linearly independent.

To know more about vectors refer here:

https://brainly.com/question/13322477

#SPJ11

r ≈ 12 meters is your answer :)

Anyway, it is from this formula: V=πr^ 2   h/ 3

it is actually ≈ 11.99696m

Answer:

3/700

Step-by-step explanation:

hope this helps :))

Ryan, a consumer electronics​ salesperson, earns a base wage of ​$ 1300 per month and a commission of 7​% on the amount of sales he makes. One month Ryan received a $1622 paycheck, which made his sales for the month $4600.

To find the amount of Ryan's sales for the month, we can use the equation:

Total paycheck = Base salary + (Commission rate × Sales)

We can plug in the given values and solve for the amount of sales:

$1622 = $1300 + (0.07 × Sales)

$322 = 0.07 × Sales

Sales = $322 ÷ 0.07

Sales = $4600

Therefore, Ryan's sales for the month were $4600.

You can learn more about amount of sales at

https://brainly.com/question/29110387

#SPJ11

Trigoometric function

1) To find a value of theta that satisfies the statement, we can rearrange the equation and use the double angle formula for cosine:

cos(π/2-theta)=1/7

cos(π/2)cos(theta)+sin(π/2)sin(theta)=1/7

0cos(theta)+1sin(theta)=1/7

sin(theta)=1/7

theta=sin^-1(1/7)

theta=8.213 degrees or 0.143 radians

Therefore, a value of theta that satisfies the statement is 0.143 radians.

2) To find all values of theta that satisfy the statement, we can use the fact that sin(theta) is negative in the third and fourth quadrants:

sin(theta)=-√3/2

theta=sin^-1(-√3/2)

theta=4π/3 or 5π/3

Therefore, the values of theta that satisfy the statement are 4π/3 and 5π/3.

Learn more about Trigonometric functions:

brainly.com/question/6904750

#SPJ11

The area of the trapezoid in simplest radical form is 78 feet².

Given a trapezoid.

Length of the bases are 10 feet and 16 feet.

We have to find the height.

Consider the smaller right triangle formed by the height of the trapezoid.

Triangle base length or one leg = 16 - 10 = 6 feet

Since one of the angle is 45°, the other angle in the right triangle is also 45°.

Since it is isosceles, opposite sides for 45° angles are same.

Other leg = 6 feet, which is the height.

Area of the trapezoid = 1/2 (a + b)h, where a and b are bases and h is the height.

A = 1/2 (10 + 16) 6

   = 78 feet²

Hence the correct option is b.

Learn more about Area here :

https://brainly.com/question/12221769

#SPJ1

y = 2.50 / (1 + 15.80^−x)

You can use technology to approximate the given data with a logistic regression curve y = N/(1 + Ab^−x).

To do this, you'll need to calculate the parameters A, N, and b. To calculate A and N, you can use the values of y at the extremes of x. At x = 0, y = 3.0 and at x = 150, y = 9.9. So, A = (9.9 - 3.0) / (1 - 0.003^150) and N = 9.9 - A*0.003^150. Then, b can be calculated using the average of the logarithm of all x values. The final logistic regression curve will be:

y = 2.50 / (1 + 15.80^−x)

Learn more about  logistic regression curve

brainly.com/question/26677807

#SPJ11

Answer: The representations of these functions are alike in that they both describe the movement of the falling object. They are different in that one function measures the distance the object has traveled from its starting point, while the other measures its distance from the ground.

Step-by-step explanation:

To solve the absolute value inequality, we need to isolate the absolute value expression on one side of the inequality and then solve for x. Here are the steps:

4| x +3| + 6 < 2

4| x +3| < -4 (Subtract 6 from both sides)

| x +3| < -1 (Divide both sides by 4)

Since the absolute value of any expression is always positive, there is no solution to this inequality. In interval notation, we can write the solution as ∅ (empty set).

Answer: ∅  

To know more about absolute value equations and inequalities, check out:

brainly.com/question/1779337

#SPJ11

Answer:

x = 10.25

Step-by-step explanation:

congruent angles are equal , then

18x - 34 = 10x + 48 ( subtract 10x from both sides )

8x - 34 = 48 ( add 34 to both sides )

8x = 82 ( divide both sides by 8 )

x = 10.25

The length and width of the rectangle are 10 and 3, respectively.

Let's use "l" to represent the length of the rectangle and "w" to represent the width. From the problem statement, we've got portions of information:

The perimeter is 26. The formulation for the perimeter of a rectangle is P = 2l + 2w. So we are able to write:

2l + 2w = 26

The length is four extra than twice the width. In equation shape:

l = 2w + four

Now we can use substitution to resolve for the length and width. we will alternative the expression 2w + 4 for l within the first equation:

2(2w + 4) + 2w = 26

Simplifying:

4w + 8 + 2w = 26

6w + 8 = 26

6w = 18

w = 3

So the width of the rectangle is three. To discover the length, we're going to substitute w = 3 into the equation for l:

l = 2w + 4 = 2(3) + 4 = 10

So the length of the rectangle is 10.

Thus, the length and width of the rectangle are 10 and 3, respectively.

Learn more about Perimeter of rectangle formula:-

https://brainly.com/question/20853439

#SPJ4

The equation of the line in slope-intercept form is y = -x + 1

To write an equation for the line in point-slope form, we can use the formula y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.

Since the x-intercept and y-intercept are both 1, we know that the line passes through the points (1,0) and (0,1).

To find the slope of the line, we can use the formula m = (y2 - y1) / (x2 - x1). Plugging in the coordinates of the two points, we get:

m = (1 - 0) / (0 - 1) = -1

Now we can plug in the slope and one of the points into the point-slope form equation:

y - 0 = -1(x - 1)

Simplifying, we get:

y = -x + 1

This is the equation of the line in point-slope form.

To write the equation in slope-intercept form, we can use the formula y = mx + b, where m is the slope of the line and b is the y-intercept.

We already found the slope to be -1, and the y-intercept is given as 1. So we can plug these values into the slope-intercept form equation:

y = -1x + 1

Simplifying, we get:

y = -x + 1

This is the equation of the line in slope-intercept form.

To know more about slope-intercept form click on below link:

https://brainly.com/question/29146348#

#SPJ11

a)not linear

b)linear

c)not linear

d)linear

(i) T:R2→R2 defined by T(x,y)=(x,∣x+y∣): This transformation is not linear because it is not closed under addition and scalar multiplication.

(ii) T:Rn→R defined by T(x)=a⋅x, where a is a fixed vector of Rn: This transformation is linear because it is closed under addition and scalar multiplication.

(iii) T:P2(R)→P2(R) where (T(f))(x)=f(x)+x: This transformation is not linear because it is not closed under addition and scalar multiplication.

(iv) T:Rn→R defined by T(x)=xTa, where a is a fixed vector of Rn: This transformation is linear because it is closed under addition and scalar multiplication.

Learn more about linear transformation equation

brainly.com/question/30170459

#SPJ11

The T(αu + v) = αT(u) + T(v), and so T is linear.

(i) Transformation T: R2 → R2 defined by T(x,y) = (x,|x + y|) is not linear, as the following counterexample proves: let u = (1,1) and v = (−1,2) be vectors in R2. Then:
T(u) = T(1,1) = (1,|1 + 1|) = (1,2)
T(v) = T(−1,2) = (−1,|−1 + 2|) = (−1,1)
However,
T(u + v) = T(1 − 1, 1 + 2) = T(0,3) = (0,|0 + 3|) = (0,3)
T(u) + T(v) = (1,2) + (−1,1) = (0,3)
Thus, T(u + v) ≠ T(u) + T(v), and so T is not linear.

(ii) Transformation T: Rn → R defined by T(x) = a · x, where a is a fixed vector of Rn, is linear. This can be easily checked by verifying that for any vectors x and y in Rn and scalars α and β in R, we have:
T(αx + βy) = a · (αx + βy) = α(a · x) + β(a · y) = αT(x) + βT(y)

(iii) Transformation T: P2(R) → P2(R) where (T(f))(x) = f(x) + x is linear. We can prove this as follows. Let f and g be any polynomials in P2(R) and let α be any scalar in R. Then:
(T(αf + g))(x) = (αf + g)(x) + x = αf(x) + g(x) + x = α(T(f))(x) + (T(g))(x)
Thus, T(αf + g) = αT(f) + T(g), and so T is linear.

(iv) Transformation T: Rn → R defined by T(x) = xT a, where a is a fixed vector of Rn, is linear. We can prove this as follows. Let u and v be any vectors in Rn and let α be any scalar in R. Then:
T(αu + v) = (αu + v)T a = α(uT a) + vT a = αT(u) + T(v)
Thus, T(αu + v) = αT(u) + T(v), and so T is linear.

Learn more about Linear

brainly.com/question/15830007

#SPJ11

According to the figure the congruent angles are: ∠BAC = ∠CDB, ∠ABD = ∠ACD, ∠ACB = ∠ADB and ∠CBD = ∠CAD

Congruent angles may be define as if two or more angles measures the same value. In other words, if two angles are congruent, they will have the same degree measure, and they will look identical when placed on top of each other. This is similar to the concept of congruent shapes or figures, where two shapes have the same size and shape.

According to the figure the points A, B, C, and D are consecutive points on Circle W (center) as shown in figure.

We need to find out the angles must be congruent to the angles of ABD, BAC, ACB and CBD.

according to the figure we have to get some values of congruent angles are:

∠BAC = ∠CDB,

∠ABD = ∠ACD,

∠ACB = ∠ADB and

∠CBD = ∠CAD

To know more about Circle, Visit:

https://brainly.com/question/8952990

#SPJ1

Q3) The correct answer is 0.30.

Q2) (a) The sample space for three True or False questions is:
TTT, TTF, TFT, TFF, FTT, FTF, FFT, FFF

Q2) The outcomes corresponding to the event "The student answered True at least two times" are:
TTT, TTF, TFT, FTT

Q2) The probability of the student answering True at least two times is:
P(X >= 2) = 4/8 = 0.50

The probability of an item being exceptionally good is 0.20, and the probability of an item not being exceptionally good is 0.80. We can use the binomial probability formula to find the probability of exactly 2 of the 10 inspected items being exceptionally good:

P(X = 2) = (10 choose 2) * (0.20)^2 * (0.80)^8 = 45 * 0.04 * 0.16777 = 0.30

Therefore, the correct answer is 0.30.

(a) The sample space for three True or False questions is:
TTT, TTF, TFT, TFF, FTT, FTF, FFT, FFF

(b) The outcomes corresponding to the event "The student answered True at least two times" are:
TTT, TTF, TFT, FTT

(c) The probability of the student answering True at least two times is:
P(X >= 2) = 4/8 = 0.50

Therefore, the correct answer is 0.50.

Learn more about Probability

brainly.com/question/30034780

#SPJ11

The distance between Seaside and Samuel's house is approximately 77.8 kilometers.

To find the distance between Seaside and Samuel's house, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is the distance between Seaside and Samuel's house, and the other two sides are the distances from Stafford to Samuel's house and from Stafford to Seaside.

1. Let x be the distance between Seaside and Samuel's house.

2. According to the Pythagorean theorem, x^2 = 24^2 + 74^2

3. Simplifying the equation gives us x^2 = 576 + 5476

4. Further simplifying gives us x^2 = 6052

5. Taking the square root of both sides gives us x = 77.8

Therefore, the distance between Seaside and Samuel's house is approximately 77.8 kilometers

Learn more about Pythagorean theorem at

https://brainly.com/question/24252852

#SPJ11

Answer:

y=2500(0.15)^x

y=375^x

Step-by-step explanation:

Shiro purchased 11 pounds of beef and 4 pounds of chicken.

Shiro purchased a total of 18 pounds of meat, spending $96.

We can designate the beef as x pounds, and the chicken as y pounds. To find the solution, we set up two equations:

6x + 4.5y = 96 x + y = 18

To solve this system of equations, we can subtract 6x from both sides of the first equation, giving us 4.5y = 96 - 6x.

We can substitute this expression into the second equation, giving us x + (96 - 6x) = 18.

We can then simplify this equation, giving us 7x = 78, and thus x = 11.

Now we can substitute x = 11 into the original equation, 6x + 4.5y = 96, to find y = 4.

Therefore, Shiro purchased 11 pounds of beef and 4 pounds of chicken.

Learn more about equation at

https://brainly.com/question/22277991

#SPJ11

The probability of spinning an even number is 39/10

The missing barchart is added as an attachment

The bar chart (see attachment) represents the graph that would be used to calculate the required probability

On the bar chart, we have the sample size of the even number

Even number = 18 + 21

Even number = 39

So, we have

P(Even) = Even/Total

By substitution. we have

P(Even) = 39/100

Hence, the probability is 39/100

Read more about probability at

https://brainly.com/question/251701

#SPJ1

To solve the inequality -3 > (x)/(4) - 1, we need to isolate the variable x on one side of the inequality. We can do this by following these steps:

Step 1: Add 1 to both sides of the inequality to eliminate the constant term on the right side.
-3 + 1 > (x)/(4) - 1 + 1
-2 > (x)/(4)

Step 2: Multiply both sides of the inequality by 4 to eliminate the fraction on the right side.
-2 * 4 > (x)/(4) * 4
-8 > x

Step 3: Rewrite the inequality with the variable on the left side.
x < -8

Therefore, the solution to the inequality is x < -8.

Note: When multiplying or dividing an inequality by a negative number, the inequality symbol must be reversed. However, in this case, we multiplied by a positive number (4), so the inequality symbol remains the same.

To know more about Inequality equation:

https://brainly.com/question/21311270

#SPJ11

For the given quadratic function the features are:

A parabola, a U-shaped curve, is the shape of a quadratic function's graph.

There are three characteristics that all quadratic functions share:

Thus, for the given quadratic function the features are:

Know more about quadratic function

https://brainly.com/question/1214333

#SPJ1

Answer:              The equation is 117 = 2x + (x + 12) + (3x - 9)         The two short sides are 19 cm long, the third side is 31 cm long, and the fourth side is 48 cm long.

Step-by-step explanation:

Let x represent the length of the shortest sides

The equation for the problem is:

117 = 2x + (x + 12) + (3x - 9)

Simplify:

117 = 6x + 3

114 = 6x

19 = x

Plug x in for all the sides:

Short sides = 19 cm

Third side = (19) + 12 = 31 cm

Fourth side = 3(19) - 9 = 57 - 9 = 48 cm

Sentence:

The two short sides are 19 cm long, the third side is 31 cm long, and the fourth side is 48 cm long.

Hope this helps!

The value of x and y are

x=100° y=100°

In an equilateral triangle,

Each angle = 60°

∴ a + a + 100° = 180°

⇒ 2a + 100° = 180°

⇒ 2a = 180° – 100° = 80°

∴ a = 80°/2 = 40° ∴ x = 60° + 40° = 100°

And y = 60° + 40° = 100°

An equilateral triangle in geometry is a triangle with equally long sides. The three angles opposite the three equal sides are equal in size because the three sides are equal. As a result, with each angle measuring 60 degrees, it is sometimes referred to as an equiangular triangle. Equilateral triangles have the same area, perimeter, and height formula as other kinds of triangles.

An equilateral triangle has a predictable shape. By combining the words "Equi" (which means equal) and "Lateral," which refers to sides, the word "Equilateral" is created. Due to the equality of its sides, an equilateral triangle is also known as a regular polygon or regular triangle.

from the question:

In an equilateral triangle,

Each angle = 60°

Let each base angle = a

∴ a + a + 100° = 180°

⇒ 2a + 100° = 180°

⇒ 2a = 180° – 100° = 80°

∴ a = 80°/2 = 40° ∴ x = 60° + 40° = 100°

And y = 60° + 40° = 100°

to learn more about equilateral triangles visit

https://brainly.com/question/3461022

#SPJ1

complete question

Apply the properties of equilateral triangles and find the values of x and y in the given figure